Question

The marks obtained by 50 students in Mathematics are given below.

(i) Make a frequency distribution table taking a class size of 10 marks

(ii) Draw a histogram and a frequency polygon.

52	33	56	52	44	59	47	61	49	61
47	52	67	39	89	57	64	58	63	65
32	64	50	54	42	48	22	37	59	63
36	35	48	48	55	62	74	43	41	51
08	71	30	18	43	28	20	40	58	49

Answer 1

Maximum marks obtained = 89

Minimum marks obtained = 08

Range = Maximum marks – Minimim marks

= 89 – 08

= 81

Taking the class size = 10, then

Number of possible intervals = `"Range"/"Class size"`

= `81/10`

= 8.1

= 9

Class Interval	Tally marks	Frequency
0 − 10	I	1
10 − 20	I	1
20 − 30	III	3
30 − 40	IIII III	8
40 − 50	IIII IIII III	13
50 − 60	IIII IIII II	12
60 − 70	IIII IIII	9
70 − 80	II	2
80 − 90	I	1
Total	50	50

Now we have the continuous frequency table.

Class Intervals	0 − 10	10 − 20	20 − 30	30 − 40	40 − 50	50 − 60	60 − 70	70 − 80	80 − 90
Frequency	1	1	3	8	13	12	9	2	1

We will draw the histogram taking class interval in x-axis and frequency in y-axis as follows.